Tenenbaum and Raffman (2012) claim that "most of our projects and ends are vague." (p.99) But I'm not convinced that any plausibly are. On my own blog, I recently discussed the self-torturer case, and how our interest in avoiding pain is not vague but merely graded. I think similar things can be said of other putative "vague" projects.
T&R's central example of a vague project is writing a book:
Suppose you are writing a book. The success of your project is vague along many dimensions. What counts as a sufficiently good book is vague, what counts as an acceptable length of time to complete it is vague, and so on. (p.99)
You may wish for a restful night’s sleep, but to stay up as late as possible as is consistent with that. Since restful is vague, one minute of sleep apparently couldn’t make the difference between a restful and a nonrestful night, and you ought to stay up for another minute. But foreseeably, if you keep thinking that way, you will stay up all night. (p.474)
As with the book case, this strikes me as simply involving a trade-off between two graded (non-vague) ends. To speak of a "wish for a restful night's sleep" is surely just a rough shorthand for what is really a graded desire, for a night's sleep that is more restful rather than less so. Perhaps there are some threshold effects in there, insofar as some lost minutes may have more noticeable effects than others on your state of mind the next day (and you can't know in advance exactly which minutes these are). But it's clearly just false to assume that a minute's less sleep will always make no difference to what it is that you really want here (regardless of whether the term 'restful' still applies to your night's sleep -- there's clearly more to your interest in a restful night's sleep than just the binary question of whether it was restful or not).